The App Store won't let me open 1Password, instead asking me to enter an old Apple ID.
Control-click in Finder brings up the same message. Subscribed directly from 1Password, not he App Store.
Have I been hacked? Or is this a glitch?
I'm running Sierra.
If you didn't get 1Password from the App Store then you shouldn't expect to open it from there. (Often the features of an app in the App Store may differ slightly from that app bought directly from the developer). If you obtained 1Password from 1password.com or agile bits.com (which will redirect you to 1password.com as they are the developer) then you should try to open it using the password you did set up. If you can't remember what the password is, you might try contacting the developer directly. https://support.1password.com/forgot-account-password/
Sorry, I may be missing something. I don't see why the App Store is involved at all. If you bought 1Password directly from the developer it should be installed in the applications folder. Possibly the very first app there. So if you double click on its icon there, what happens?